Reidemeister moves

Is it a knot, or not a knot? Reidermeister moves help you resolve such a dilemma. Mathematical knots can be rather deceitful when they're complicated. What looks like a knot may in fact be an unknot. It may be possible to untangle the thing until it becomes a perfect loop, an unknot. It is quite difficult to tell just by visualizing the questionable knot. One way of determining its knotishness is by making a physical model of it and tugging away until you're out of ideas. Another way is to make a 2-dimensional projection of the knot (its shadow) and examine the crossings. When untangling a pseudo-knot, there are three possible moves that could eventually give you an unknot. These moves are called Reidemeister moves. They look somewhat like this: